WASHINGTON – Construction of new homes edged up slightly in September, helped by a rebound in single-family construction. But applications for building permits fell by the largest amount in five months, a worrisome sign for future housing work.

The Commerce Department said Tuesday that construction of new homes and apartments rose 0.5 percent in September to a seasonally adjusted annual rate of 590,000 units. That was a weaker showing than the 610,000 economists had expected.

New applications for building permits, considered a good sign of future activity, fell 1.2 percent in September.

That’s the biggest decline since a 2.5 percent drop in April and underscored worries the fledgling housing revival could be derailed by rising unemployment and the expiration on Nov. 30 of the government’s $8,000 tax credit for first-time homebuyers.

The drop in wholesale prices was another sign the recession had kept a lid on inflation. Last week, the government said consumer prices edged up a modest 0.2 percent in September.

Housing has been struggling to recover this year following a steep collapse that helped pull the overall economy into the worst recession since the 1930 s.

But the industry still faces high unemployment, tighter bank lending standards and worries that home sales could falter once the a tax credit of up to $8,000 for first-time homebuyers expires at the end of next month. Real estate agents and homebuilders are lobbying Congress to extend the credit.

That effort appears to be gaining momentum, but the administration is being vague about its position.

Housing Secretary Shaun Donovan said in written testimony for a congressional hearing Tuesday that supporting the housing market “can be very expensive, especially at a time of significant budget deficits.” The administration “will work with Congress to fashion appropriate and effective home buyer incentives,” he added.

Some analysts and lawmakers are skeptical about extending the credit, arguing that most homebuyers who receive it would have decided to buy anyway. And soaring unemployment is likely to dull the impact of any extension, Mark Vitner, a senior economist with Wells Fargo Securities, wrote in a note to clients.

“Many of the most likely buyers targeted have already taken advantage of the program,” he wrote.

The 0.5 percent rise in overall construction in September followed a 1 percent drop in August that was revised down from an initial estimate of a 1.5 percent gain.

Construction of single-family homes rose 3.9 percent last month to an annual rate of 501,000 units, reversing a 4.7 percent drop in August. Multifamily construction, a much smaller and more volatile segment, posted a 15.2 percent drop following a 20.7 percent rise in August.

Construction rose 7.1 percent in the South, but all other regions showed weakness. Building activity fell 5.5 percent in the Northeast, 1.8 percent in the Midwest and 8.8 percent in the West.

An index from the National Association Home Builders that measures builder confidence slipped slightly in October to a reading of 18, from 19 in September. Builders blamed the slippage on the approaching expiration of the homebuyer tax credit.

The industry contends that extending and expanding the credit for one year would generate nearly 350,0000 jobs and $11.6 billion in additional tax revenues.